Drawing Many-Pointed Stars

Many programming courses start by teaching how to create programs that execute mathematical calculations. While applications to calculations are the historical origins of computer programming, and we'll see plenty of that eventually, we want to introduce you to Python, and programming in general, in a more creative context: drawing.

Drawing Many-Pointed Stars

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Drawing Many-Pointed Stars

Run the code below! What does it draw?

from turtle import *
color('red')

for i in range(20):
    forward(200)
    left(108)

bye()

Python 3

Drawing Many-Pointed Stars

The navigational commands are similar to the maze game, but now you need more careful control to specify exactly how far the turtle moves as it draws and how much it turns. The numbers in parentheses are sample values that can be set freely:

forward(150) makes it move 150 pixels forward (in the direction it is presently facing)
left(60) makes it turn (on the spot) 60 degrees to the left (counterclockwise)
Similarly, right(60) makes it turn 60 degrees to the right

One important, unintuitive note:

The turning angle inside the left (and right) commands is not the interior angle of the turn. Rather, it is how much the turtle turns from the direction it had previously been facing.

So to make this really sharp turn, you use the command left(170).

Drawing Many-Pointed Stars

Try to figure this one out before you hit "Run code," then run the code to check your answer.

What will this program draw?

from turtle import *
color('red')

for i in range(6):
    forward(300)
    left(120)

bye()

Python 3

Drawing Many-Pointed Stars

Drawing a 20-point star would take you quite a while with paper and pencil, but with a carefully constructed drawing program, you don't even have to list the steps in the code 20 times! Instead, this little program uses a loop to repeat two instructions over and over:

forward(200) means "move forward 200 pixels."
left(216) means "turn counterclockwise 216 degrees."

And the line just before these directions, for i in range(20):, is the line that controls the loop and specifies how many times the immediately following instructions get repeated: 20 times.

Run the code below and then change the 20 to 5 so that the instructions to move forward and turn 216 degrees only repeat five times instead of 20. What's the difference between the star that's drawn in each case?

from turtle import *
color('red')

for i in range(20):
    forward(200)
    left(216)

bye()

Python 3

Drawing Many-Pointed Stars

Here is the same program again. Your task now is to figure out how to set the three numbers below to make a 20-point star.

Hint: If you evenly space 20 points around a circle, zig-zagging from one side of the circle to a point almost, but not-exactly across and then back again makes an 18 degree angle.

What is the smallest positive value that you can you set the left turning angle to if your goal is to draw a 20-point star?

from turtle import *
color('red')

for i in range(20):
    forward(200)
    left(216)

bye()

Python 3

Drawing Many-Pointed Stars

Now how could we change the color of the star? E. g. make it purple, or green? Which line could you edit to change the star's coloring?

from turtle import *
color('red')

for i in range(20):
    forward(200)
    left(216)

bye()

Python 3

Drawing Many-Pointed Stars

This course will cover loops, nested loops, conditionals, and recursion! While the structure of a single loop may be simple, learning how to plan out and manage the control-flow of your programs is one of the toughest parts of programming.

That's all for now, but you're welcome to explore this star-drawing program a bit more on your own before continuing!

Challenge 1: What happens if you alternate between two different edge lengths?
(Run the code below to see.)
Challenge 2: What happens if you alternate between two different turn angles?
Challenge 3: Can you make a 12-point star that's perfectly symmetric?

Loops can execute any number of instructions, just make sure that each instruction is on its own line and indented once inwards from the loop header, for i in range(5):.

from turtle import *
color('red')

for i in range(5):
    forward(200)
    left(216)
    forward(150)
    left(216)

bye()

Python 3

Excel in math and science

Master concepts by solving fun, challenging problems.

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Programming with Python

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Drawing Many-Pointed Stars